Let the mass of planet be mp and that of earth be m .
Given, mp=2m
Density of planet (ρp)= Density of earth (ρ) As we know that, Weight of object on earth is W w=mg⋅⋅⋅⋅⋅⋅⋅(i) where, g is acceleration due to gravity.
and g=
Gm
R2
where, G= universal gravitational constant, R= radius of earth and me= mass of earth. ⇒g=
Gρ
4
3
πR3
R2
⇒g=Gρ
4
3
πR Putting this value in Eq. (i), we get w=mGρ
4
3
πR⋅⋅⋅⋅⋅⋅⋅(ii)
As densities of planets earth is same. i.e., ρp=ρ ⇒
mp
4
3
πRp3
=
m
4
3
πR3
⇒Rp=(
mp
m
R3)1∕3 =(
2m
m
R3)1∕3 ⇒Rp=(2)1∕3R Weight on planet, wp=
4
3
(2)1∕3πmGρR⋅⋅⋅⋅⋅⋅⋅(iii) Dividing Eq. (iii) by Eq. (ii), we get